What is the derivative of \sqrt[3]{(5x+pi^2^4}) ?

The derivative of \sqrt[3]{(5x+pi^2^4}) is (20(5x+pi^2)^{1/3})/3

What is the first derivative of \sqrt[3]{(5x+pi^2^4}) ?

The first derivative of \sqrt[3]{(5x+pi^2^4}) is (20(5x+pi^2)^{1/3})/3

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\frac{20 ( 5 x + π ^{2} ) ^{\frac{1}{3}}}{3}

Solution steps

Apply the chain rule:

\frac{1}{3 ( ( 5 x + π ^{2} ) ^{4} ) ^{\frac{2}{3}}} \frac{d}{d x} ((5 x + π^{2})^{4})

= \frac{1}{3 ( ( 5 x + π ^{2} ) ^{4} ) ^{\frac{2}{3}}} \frac{d}{d x} ((5 x + π^{2})^{4})

\frac{d}{d x} ((5 x + π^{2})^{4}) = 20 (5 x + π^{2})^{3}

= \frac{1}{3 ( ( 5 x + π ^{2} ) ^{4} ) ^{\frac{2}{3}}} \cdot 20 (5 x + π^{2})^{3}

Simplify

\frac{1}{3 ( ( 5 x + π ^{2} ) ^{4} ) ^{\frac{2}{3}}} \cdot 20 (5 x + π^{2})^{3} : \frac{20 ( 5 x + π ^{2} ) ^{\frac{1}{3}}}{3}

= \frac{20 ( 5 x + π ^{2} ) ^{\frac{1}{3}}}{3}

x \to 0 lim (x^{3} + 5)

\frac{3}{( s ^{2} + 4 s + 13 )}

\frac{d y}{d x} - (sin (x)) y = 2 sin (x)

f (x) = cos^{2} (x) - 2 sin (x)

\int_{0}^{\infty} cos (π x) d x

What is the derivative of \sqrt[3]{(5x+pi^2^4}) ?
The derivative of \sqrt[3]{(5x+pi^2^4}) is (20(5x+pi^2)^{1/3})/3
What is the first derivative of \sqrt[3]{(5x+pi^2^4}) ?
The first derivative of \sqrt[3]{(5x+pi^2^4}) is (20(5x+pi^2)^{1/3})/3